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A196856 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,1,0,2,4 for x=0,1,2,3,4.

%I A196856 #7 Jun 02 2025 04:35:25
%S A196856 1,2,2,4,11,4,6,38,38,6,12,136,206,136,12,22,496,1370,1370,496,22,40,
%T A196856 1792,8767,16876,8767,1792,40,74,6440,56470,199125,199125,56470,6440,
%U A196856 74,136,23306,363685,2369631,4326720,2369631,363685,23306,136,250,84180
%N A196856 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,1,0,2,4 for x=0,1,2,3,4.
%C A196856 Every 0 is next to 0 3's, every 1 is next to 1 1's, every 2 is next to 2 0's, every 3 is next to 3 2's, every 4 is next to 4 4's
%C A196856 Table starts
%C A196856 ...1......2........4...........6.............12...............22
%C A196856 ...2.....11.......38.........136............496.............1792
%C A196856 ...4.....38......206........1370...........8767............56470
%C A196856 ...6....136.....1370.......16876.........199125..........2369631
%C A196856 ..12....496.....8767......199125........4326720.........94652804
%C A196856 ..22...1792....56470.....2369631.......94652804.......3805929995
%C A196856 ..40...6440...363685....28194191.....2069281146.....152929723254
%C A196856 ..74..23306..2343584...335586650....45250654402....6148984299163
%C A196856 .136..84180.15108610..3993458371...989582452566..247223213832440
%C A196856 .250.303664.97376923.47516896629.21641093339471.9939022894905148
%H A196856 R. H. Hardin, <a href="/A196856/b196856.txt">Table of n, a(n) for n = 1..144</a>
%e A196856 Some solutions for n=6 k=4
%e A196856 ..0..0..0..2....0..0..0..0....0..0..0..0....0..0..0..2....0..0..0..1
%e A196856 ..0..0..0..0....0..0..1..2....0..0..2..2....0..0..0..0....0..0..0..1
%e A196856 ..1..1..2..0....2..2..1..0....1..1..2..0....0..0..1..1....2..1..1..0
%e A196856 ..0..0..2..2....0..0..2..2....0..0..0..0....0..1..0..0....0..0..2..0
%e A196856 ..2..2..0..0....1..1..0..0....0..0..1..2....2..1..0..0....0..0..1..1
%e A196856 ..0..2..0..0....0..0..0..0....0..2..1..0....0..0..0..2....0..0..2..0
%Y A196856 Column 1 is A196700
%K A196856 nonn,tabl
%O A196856 1,2
%A A196856 _R. H. Hardin_ Oct 06 2011